




"""simple docstring"""





import os
from collections.abc import Iterator

def        _UpperCamelCase     (      UpperCamelCase = "."				)      ->      Iterator[str]:


			"""simple docstring"""
			for dir_path, dir_names, filenames in os.walk(UpperCamelCase				):
						__UpperCAmelCase						:			Any												=       [d for d in dir_names if d != "scripts" and d[0] not in "._"]
						for filename in filenames:
									if filename == "__init__.py":
												continue
									if os.path.splitext(UpperCamelCase				)[1] in (".py", ".ipynb"):
												yield os.path.join(UpperCamelCase					,							UpperCamelCase				).lstrip("./"				)

def        _UpperCamelCase     (      UpperCamelCase				)      ->      Optional[int]:


			"""simple docstring"""
			return f"{i * '  '}*" if i else "\n##"

def        _UpperCamelCase     (      UpperCamelCase					,							UpperCamelCase				)      ->      str:


			"""simple docstring"""
			__UpperCAmelCase						:			Optional[int]												=       old_path.split(os.sep				)
			for i, new_part in enumerate(new_path.split(os.sep				)				):
						if (i + 1 > len(UpperCamelCase				) or old_parts[i] != new_part) and new_part:
									print(f"{md_prefix(UpperCamelCase				)} {new_part.replace('_'					,							' '				).title()}"				)
			return new_path

def        _UpperCamelCase     (      UpperCamelCase = "."				)      ->      None:


			"""simple docstring"""
			__UpperCAmelCase						:			str												=       ""
			for filepath in sorted(good_file_paths(UpperCamelCase				)				):
						__UpperCAmelCase						,  __UpperCAmelCase						:			List[str]												=       os.path.split(UpperCamelCase				)
						if filepath != old_path:
									__UpperCAmelCase						:			Tuple												=       print_path(UpperCamelCase					,							UpperCamelCase				)
						__UpperCAmelCase						:			Union[str, Any]												=       (filepath.count(os.sep				) + 1) if filepath else 0
						__UpperCAmelCase						:			Any												=       f"{filepath}/{filename}".replace(" "					,							"%20"				)
						__UpperCAmelCase						:			int												=       os.path.splitext(filename.replace("_"					,							" "				).title()				)[0]
						print(f"{md_prefix(UpperCamelCase				)} [{filename}]({url})"				)


if __name__ == "__main__":
					print_directory_md(""".""")




"""simple docstring"""


import numpy as np



def 						lowerCamelCase__      (				UpperCAmelCase_		,   UpperCAmelCase_		,   UpperCAmelCase_ = 1E-12		,   UpperCAmelCase_ = 1_00		,   )->				tuple[float, np.ndarray]:







       """simple docstring"""
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[1]
       # Ensure proper dimensionality.
       assert np.shape(UpperCAmelCase_					)[0] == np.shape(UpperCAmelCase_					)[0]
       # Ensure inputs are either both complex or both real
       assert np.iscomplexobj(UpperCAmelCase_					) == np.iscomplexobj(UpperCAmelCase_					)
       UpperCamelCase       			=		np.iscomplexobj(UpperCAmelCase_					)
       if is_complex:
              # Ensure complex input_matrix is Hermitian
              assert np.array_equal(UpperCAmelCase_		,   input_matrix.conj().T					)

       # Set convergence to False. Will define convergence when we exceed max_iterations
       # or when we have small changes from one iteration to next.

       UpperCamelCase       			=		False
       UpperCamelCase       			=		0
       UpperCamelCase       			=		0
       UpperCamelCase       			=		1E12

       while not convergence:
              # Multiple matrix by the vector.
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)
              # Normalize the resulting output vector.
              UpperCamelCase       			=		w / np.linalg.norm(UpperCAmelCase_					)
              # Find rayleigh quotient
              # (faster than usual b/c we know vector is normalized already)
              UpperCamelCase       			=		vector.conj().T if is_complex else vector.T
              UpperCamelCase       			=		np.dot(UpperCAmelCase_		,   np.dot(UpperCAmelCase_		,   UpperCAmelCase_					)					)

              # Check convergence.
              UpperCamelCase       			=		np.abs(lambda_ - lambda_previous					) / lambda_
              iterations += 1

              if error <= error_tol or iterations >= max_iterations:
                     UpperCamelCase       			=		True

              UpperCamelCase       			=		lambda_

       if is_complex:
              UpperCamelCase       			=		np.real(lambda_					)

       return lambda_, vector



def 						lowerCamelCase__      (				)->				None:







       """simple docstring"""
       UpperCamelCase       			=		np.array([[41, 4, 20], [4, 26, 30], [20, 30, 50]]					)
       UpperCamelCase       			=		np.array([41, 4, 20]					)
       UpperCamelCase       			=		real_input_matrix.astype(np.complexaaa					)
       UpperCamelCase       			=		np.triu(1j * complex_input_matrix		,   1					)
       complex_input_matrix += imag_matrix
       complex_input_matrix += -1 * imag_matrix.T
       UpperCamelCase       			=		np.array([41, 4, 20]					).astype(np.complexaaa					)

       for problem_type in ["real", "complex"]:
              if problem_type == "real":
                     UpperCamelCase       			=		real_input_matrix
                     UpperCamelCase       			=		real_vector
              elif problem_type == "complex":
                     UpperCamelCase       			=		complex_input_matrix
                     UpperCamelCase       			=		complex_vector

              # Our implementation.
              UpperCamelCase			,							UpperCamelCase       			=		power_iteration(UpperCAmelCase_		,   UpperCAmelCase_					)

              # Numpy implementation.

              # Get eigenvalues and eigenvectors using built-in numpy
              # eigh (eigh used for symmetric or hermetian matrices).
              UpperCamelCase			,							UpperCamelCase       			=		np.linalg.eigh(UpperCAmelCase_					)
              # Last eigenvalue is the maximum one.
              UpperCamelCase       			=		eigen_values[-1]
              # Last column in this matrix is eigenvector corresponding to largest eigenvalue.
              UpperCamelCase       			=		eigen_vectors[:, -1]

              # Check our implementation and numpy gives close answers.
              assert np.abs(eigen_value - eigen_value_max					) <= 1E-6
              # Take absolute values element wise of each eigenvector.
              # as they are only unique to a minus sign.
              assert np.linalg.norm(np.abs(UpperCAmelCase_					) - np.abs(UpperCAmelCase_					)					) <= 1E-6


if __name__ == "__main__":
      import doctest

      doctest.testmod()
      test_power_iteration()





